Spherical designs and lattices

Start: 12/08/2015 - 12:15pm

End: 12/08/2015 - 1:10pm

Speaker:

Hiren Maharaj (Pomona College)

Abstract:

Let n > 1. A collection of points P on the unit sphere S_{n-2} in R^{n-1} is called a spherical t-design for some positive integer t if the average value of every polynomial in n-1 variables with real coefficients of degree t or less on S_{n-2} equals the average value of f on the set P. A full-rank lattice in R^{n-1} is called strongly eutactic if its set of normalized minimal vectors forms a spherical 2-design. Given a finite Abelian group G of order n, one can form a corresponding lattice L_G of rank n-1. This talk will be about recent joint work with Albrecht Boettcher, Lenny Fukshansky and Stephan Garcia, in which we show that L_G is strongly eutactic if and only if n is odd or G=(Z/2Z)^k for some positive integer k.